Ever since 1979, the Lyndon LaRouche organization has been running candidates in Democratic primaries. One of its most successful candidates in recent years has been Kesha Rogers, who won the Democratic U.S. House nomination in the Texas 22nd district in both 2010 and 2012. She has filed to run in the Texas Democratic primary for U.S. Senate in 2014. See this Dallas News story. Thanks to Larry Ferenz for the link.